I have the polynomial P(x) = 2*x^2 + 3*x + 4, and I'm trying to find
all values of x for which P is a perfect square. Are there infinite
values of x that generate perfect squares for P? Is there a formula
to generate those x values? From there, is there a general formula
for P(x) = a*x^2 + b*x + c?

Given x^2==a(mod p), let p be an odd prime. There are exactly (p -
1)/2 incongruent quadratic residues of p and exactly (p - 1)/2
quadratic nonresidues of p. Can you provide an example that helps
explain this concept?